For me, listening to music must be an event rather than something going on in the background. I want to be distracted by it, pulled into it, wowed by the skill of the musicians etc. The Audionet does this, the CH doesn't, simple as that.
The harder bit is to analyse why. What I think is going on is that the Audionet has a very slight emphasis on the leading edge of notes. This gives a realism to the music and imbues it with dynamics and presence. It's perhaps most evident when you hear a bass drum or timpani beat as there is an initial attack or bite to the sound which, importantly to the OP's question, happens at lower volumes as well as "realistic" volumes. I should add that in no way is this fatiguing - the cleaness and lack of distortion with these amps mean this never occurs.
I didn't get this with the CH amps, and as such, they didn't grab my attention in the way I am seeking.